$76$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $17$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 76}$ ${x = 2y-17}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-17}$ for $x$ in the first equation. ${(2y-17)}{+ y = 76}$ Simplify and solve for $y$ $ 2y-17 + y = 76 $ $ 3y-17 = 76 $ $ 3y = 93 $ $ y = \dfrac{93}{3} $ ${y = 31}$ Now that you know ${y = 31}$ , plug it back into ${x = 2y-17}$ to find $x$ ${x = 2}{(31)}{ - 17}$ $x = 62 - 17$ ${x = 45}$ You can also plug ${y = 31}$ into ${x+y = 76}$ and get the same answer for $x$ ${x + }{(31)}{= 76}$ ${x = 45}$ There were $45$ home team fans and $31$ away team fans.